Simplify the following expression: $ t = \dfrac{7}{10} + \dfrac{-r + 3}{r + 10} $
In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{r + 10}{r + 10}$ $ \dfrac{7}{10} \times \dfrac{r + 10}{r + 10} = \dfrac{7r + 70}{10r + 100} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{-r + 3}{r + 10} \times \dfrac{10}{10} = \dfrac{-10r + 30}{10r + 100} $ Therefore $ t = \dfrac{7r + 70}{10r + 100} + \dfrac{-10r + 30}{10r + 100} $ Now the expressions have the same denominator we can simply add the numerators: $t = \dfrac{7r + 70 - 10r + 30}{10r + 100} $ $t = \dfrac{-3r + 100}{10r + 100}$